Multifractal Characteristics Research Articles

Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations

We provide real-space and Fock-space (FS) characterizations of ergodic, nonergodic extended (NEE) and many-body localized (MBL) phases in an interacting quasiperiodic system, namely, the generalized Aubry-Andr\'e-Harper model, which possesses a mobility edge in the noninteracting limit. We show that a mobility edge in the single-particle (SP) excitations survives even in the presence of interaction in the NEE phase. In contrast, all single-particle excitations get localized in the MBL phase due to the MBL proximity effect. We give complementary insights into the distinction of the NEE states from the ergodic and MBL states by computing local FS self-energies and decay length associated, respectively, with the local and the nonlocal FS propagators. Based on a finite-size scaling analysis of the typical local self-energy across the NEE to ergodic transition, we show that MBL and NEE states exhibit qualitatively similar multifractal character. However, we find that the NEE and MBL states can be distinguished in terms of the distribution of local self-energy and the decay of the nonlocal propagator in the FS, whereas the typical local FS self-energy cannot tell them apart.

Evaluating structural, morphological, and multifractal aspects of n-ZnO/p-ZnO homojunctions and n-ZnO/p-NiO heterojunctions.

We have investigated the evolution of the structure and surface morphology of n-ZnO/p-ZnO homojunctions and n-ZnO/p-NiO heterojunctions transparent structures deposited by radio frequency-sputtering on quartz (Q)/ITO substrates. X-ray diffraction (XRD) analysis of the as-deposited and annealed ZnO, n-ZnO/p-NiO/Q/ITO, and n-ZnO/p-ZnO/Q/ITO thin films showed that ZnO had a wurtzite hexagonal structure and (002) preferred growth direction. The annealing temperature played a key role in improving the crystalline structure of the films, as evidenced by the changes in the intensity and position of the XRD (002) peak. Morphological analysis revealed that the roughness of the film varies with increasing annealing temperature. Particle size dictates the vertical growth of p-ZnO homojunctions, while particle shape dictated the p-NiO heterojunctions growth. Fractal analysis showed that p-ZnO homojunctions have similar spatial complexity, surface percolation, and topographical uniformity and are dominated by low dominant frequencies. Moreover, a robust multifractal character was observed, where n-ZnO/p-ZnO homojunctions follow similar vertical growth dynamics, which differed from the n-ZnO/p-NiO heterojunctions growth dynamics. These results prove that annealing temperature plays a key role in the n-ZnO/p-ZnO homojunctions and n-ZnO/p-NiO heterojunctions structure, surface morphology, and vertical growth dynamics.

Research on Multifractal Characteristics of Vehicle Driving Cycles

Vehicle driving cycles have complex characteristics, but there are few publicly reported methods for their quantitative characterization. This paper innovatively investigates their multifractal characteristics using the fractal theory to characterize their complex properties, laying the foundation for applications such as vehicle driving cycle feature identification, vehicle energy management strategies (EMS), and so on. To explore the scale-invariance of the vehicle driving cycles, the four vehicle driving cycles were analyzed using the Multifractal Detrended Fluctuation Analysis (MF-DFA) method, three of which are standard vehicle test cycles: the New European Driving Cycle (NEDC), the World-wide harmonized Light-duty Test Cycle (WLTC) and the China Light-duty Vehicle Test Cycle for Passenger Car (CLTC-P), and the other is the Urban Road Real Driving Cycle (URRDC), which was obtained by analyzing and processing vehicle driving data collected in actual urban driving conditions. The fluctuation functions, the generalized Hurst exponents, the mass exponent spectra, the multifractal singularity spectra, and the multifractal characteristic parameters were calculated to verify the multifractal characteristics, and to quantify the fluctuation singularities of different driving cycles as the time series. The results show that the fluctuations of all four driving cycles have long-range anticorrelations and exhibit significant multifractal characteristics. The results can provide a basis for the analysis of the complexity of the vehicle driving cycles.

Multifractal characteristics and return predictability in the Chinese stock markets

Multifractal characteristics and return predictability in the Chinese stock markets

Pore throat structure heterogeneity and its effect on gas-phase seepage capacity in tight sandstone reservoirs: A case study from the Triassic Yanchang Formation, Ordos Basin

The microscopic heterogeneity of pore-throat structures in tight sandstone is a crucial parameter for understanding the transport mechanism of fluid flow. In this work, we firstly developed the new procedure to characterize the pore size distribution (PSD) and throat size distribution (TSD) by combining the nuclear magnetic resonance (NMR), cast thin section (CTS), and constant-rate mercury injection (CRMI) tests, and used the permeability estimated model to verify the full-scale PSD and TSD. Then, we respectively analyzed the fractal feature of the pore and throat, and characterized the heterogeneity of pores and throats. Finally, we elaborated the effect of the pore and throat heterogeneity on the gas-phase seepage capacity base on the analysis of the simple capillary tube model and gas-flooding experiment. The results showed that (1) The PSD and TSD of the tight sandstone sample ranged from 0.01 to 10 μm and from 0.1 to 57 μm, respectively, mainly contributed by the micropores and mesopores. Meanwhile, the permeability estimated by the PSD and TSD was consistent with the experimental permeability, and relative error was lower than 8%. (2) The PSD and TSD exhibited multifractal characteristics, and singularity strength range, Δα, could be used as the indicator for characterizing the heterogeneity of pore and throat. Furthermore, the throat of the sample showed stronger heterogeneity than that the pore. (3) The throats played an important role for the fluid transport in the tight sandstone, and the effect of the throat heterogeneity on the gas-phase seepage capacity was different under the lower and higher injection pressure. The macropores and micropores maybe respectively become the preferential migration pathways at the lower and higher injection pressure. In the end, the identification plate was established in our paper, and could be described the relationship among the throat heterogeneity, injection pressure, permeability and flow path of the gas phase in the tight sandstone.

Cross-Correlation Multifractal Analysis of Technological Innovation, Financial Market and Real Economy Indices

Technological innovation, the financial market, and the real economy are mutually promoting and restricting. Considering the interference of market-noise information, this paper applies the wavelet-denoising method of the soft- and hard-threshold compromise functions to process the original information so as to eliminate the noise information, and combines multifractal detrended cross-correlation analysis with the sliding-window approach, focusing on the change in the Hurst index and the parameter change in the multifractal spectrum to explore the interaction in between. The research results show that there is a certain cross-correlation among technological-innovation, financial-market, and real-economy indices. Firstly, the cross-correlation among them has significant multifractal characteristics rather than single-fractal characteristics. Secondly, the fractal characteristics reveal the long memory of the interaction among the three indices. Thirdly, there are also obvious differences in the degree of local chaos and volatility of the interaction. Fourthly, the cross-correlation among technological-innovation, financial-market, and real-economy indices has significant multifractal characteristics rather than single-fractal characteristics. In comparison, the cross-correlation multifractal characteristics among technological innovation, the financial market, and the real economy are time-varying, and the cross-correlation multifractal characteristics between the technological-innovation index and the real-economy index are the most obvious.

Method Selection for Analyzing the Mesopore Structure of Shale—Using a Combination of Multifractal Theory and Low-Pressure Gas Adsorption

Nitrogen adsorption experiments have been extensively applied to shale pore structure research and evaluation. The pore structure can be quantitatively characterized in accordance with the nitrogen adsorption–desorption isotherm using various calculation models, whereas the results obtained using different models can more effectively indicate the pore characteristics of shale remains unclear. Further, there has not been any unified process in the optimization of calculation models for pore size distribution (PSD). In this study, the Barret–Joyner–Halenda adsorption (BJH-AD) and BJH desorption (BJH-DE) models were used with Longmaxi Formation shale as an example. Subsequently, the density functional theory (DFT) calculations were conducted on different shale lithofacies samples. Next, the pore structure parameters and heterogeneity obtained using different models were compared, and the consistency parameters of different models were obtained in accordance with Cronbach’s alpha. The results indicated that the pore structure parameters obtained using the BJH-AD model were underestimated since the macroscopic thermodynamic theory was not applicable to this study. The DFT model showed multiple peaks in the range of 1–10 nm, whereas the BJH-DE model had a significant artificial peak in the range of 3.8 nm due to the tensile strength effect, thus suggesting that the DFT model is more capable of characterizing the pores with a pore size 10 nm lower than the BJH model. The PSD curves generated using the three models exhibited multifractal characteristics, whereas the results of the heterogeneity achieved using different models were different. Moreover, the consistency of the results of different models can be studied in depth by combining Cronbach’s alpha with various heterogeneity parameters. The DFT model exhibited high consistency in pore structure parameters and pore heterogeneity, thus suggesting that the DFT method of N2 is the optimal physical adsorption data analysis method in the shale mesoporous range. Accordingly, the nitrogen adsorption curve, the hysteresis loop shape, multifractal parameters, and Cronbach’s alpha were integrated to generate a working flow chart of the nitrogen adsorption model for N2-adsorption-model optimization.

Fractal Characterization of Brass Corrosion in Cavitation Field in Seawater

Cavitation is a physical process that produces complex effects on the machines and components working in conditions where it acts. One effect is the materials-mass loss by corrosion–erosion when components are introduced into fluids under cavitation. The analysis of the damages produced by cavitation is generally performed by using different destructive and non-destructive experimental techniques. Most studies on materials’ behavior in cavitation refer to the erosion–corrosion mechanism, and very few investigate the fissure propagation by fractal methods. None have investigated the fractal characteristics of the sample surface after erosion–corrosion or the multifractal characteristics of materials’ mass variation in time in a cavitation field. Therefore, this research proposes a computational approach to determine the pattern of materials’ damages produced by ultrasound cavitation. The studied material is a brass, introduced in seawater. Fractal and multifractal techniques are applied to the series of the absolute mass loss per surface and the sample’s micrography after corrosion. Such an approach has not been utilized for such a material in similar experimental conditions. This study emphasizes that the box dimension of the series of the absolute mass loss per surface is close to one, and its behaviour is close to a non-/monofractal. It is demonstrated that the material’s surface corrosion is not uniform, and its multifractal character is highlighted by the f(α)− spectrum and the multifractal dimensions, which have the following values: the capacity dimension = 1.5969, the information dimension = 1.49836, and the correlation dimension = 1.4670.

Modelling and assessment of the arrival and departure process at the terminal area: A case study of Chennai international airport

Airport and terminal area traffic congestion is a growing concern of the air traffic management (ATM) system. A major step towards mitigating the impacts of congestion is understanding the fluctuating arrival and departure process at airports. Exploring the intrinsic time-varying nature of the arrival and departure process enhances this understanding, hence, is instrumental in formulating operational policies for managing airport capacity and delays. This paper presents a data-driven statistical framework to investigate, understand, and model the time-varying fluctuations in the aircraft arrival and departure process. We have considered one-month data obtained from Chennai international airport operations for this study. The dynamic evolution and fluctuation characteristics of arrivals and departures are conducted using Seasonality and Multifractal Detrended Fluctuation Analysis. Six theoretical probability distributions were used to fit the observed aircraft arrivals and departures at different temporal scales using the maximum likelihood estimation method. This study also develops a G1(t)/G2(t)/KFirst Come First Serve dynamic queuing model for a day’s arrival and departure process. The results suggest that arrival and departure processes exhibit weak but visible multifractal characteristics. Fluctuations are higher at a smaller temporal scale compared to a larger scale, and the probability distributions of arrival and departure are also time-varying. The framework has universal applicability, and the insights have important implications for operational policies on the air transportation workforce and infrastructure management.

Pore characteristics and preservation mechanism of over-6000-m ultra-deep shale reservoir in the Sichuan Basin

Investigation of pore characteristics and their preservation mechanism of over 6000 m ultra-deep shale reservoirs is of significance for shale gas exploration and development in the Sichuan Basin. In this study, the pores structure and multifractal characteristics of pores for the Longmaxi shale and Qiongzhusi shale in the Sichuan Basin are well studied by using field emission scanning electron microscopy (FE-SEM), gas adsorption and multifractal analysis. The results show that: (1) Extremely strong mechanical compaction resulting from ultra-deep burial depth can lead to the homogenization of pore structure, which is characterized by the change of bubble-like OM pores to silt or fracture shape pores and the higher average pore diameter (APD) value. (2) The Longmaxi shale and Qiongzhusi shale reservoirs have the obvious multifractal nature for different pore sizes. Samples from the Longmaxi shale and Qiongzhusi shale in well CS#1 demonstrate the higher average H values and smaller average ΔD values compared with those samples in well MS#1, indicating that shale reservoir in over-pressure condition has higher connectivity and less heterogeneity. The pore preservation in over 6000 m ultra-deep shale reservoirs are influenced by several geological factors, including 1) quartz is beneficial for the preservation of pores especially for OM pores due to its supporting effect; 2) the shale reservoirs in over-pressure show many more OM pores and higher surface porosity than those in normal pressure; 3) the direct floor of Qiongzhusi shale is likely the critical geological factor affecting the pores preservation. Therefore, the Longmaxi shale with both over-pressure condition and high quartz content is likely the best target zone for deep shale gas exploration in the Sichuan Basin.

Multifractal Characteristics Analysis of Spatial State of Prefecture-Level Cities in China.

In the last 40years, Chinese cities have seen extensive development across a wide array of spheres. In this study, we applied a power-law and multifractal analysis to characterise 22 indices for 288 prefecture-level cities in mainland China. The data used to characterise the indices is representative of the year 2012. The results show that the Gross domestic product (GDP) is regular and exhibits multifractal spatial characteristics. Specifically, most developmental fields exhibit coupling in conjunction with being chaotic. Furthermore, eight indices with multifractal characteristics clearly reflect the spatial complexity of the corresponding fields and the volatility between prefecture-level cities. Overall, the tertiary industry has undergone nongeneralised development. On the other hand, the construction industry resembles a bubble economy, and the spatial layout of traditional industries has a homogenising effect in Middle and East China. This study examines China's overall spatial characteristics and states based on the above-mentioned analyses; additionally, the study focuses on the early 2010s. The contribution of this study provides a quantitative analysis paradigm based on a multifractal approach.

Pore Structure Multifractal Characteristics of Coal Reservoirs in the Central and Eastern Qinshui Basin and Influencing Factors

The heterogeneity of the pore structure of coal reservoirs affects the desorption and diffusion characteristics of coalbed methane, and determining its distribution law is conducive to improving the theory of coalbed methane development. The central and eastern parts of the Qinshui Basin are rich in coalbed methane resources, but the heterogeneity characteristics of the pore structure of coal reservoirs are not clear. NMR has the advantages of being fast, non-destructive and full-scale, and multifractal can describe the self-similarity of NMR T2 curve at different scales so as to analyze the complexity of pore distribution. Based on this, 15 samples with different coal ranks were collected from the central and eastern Qinshui Basin (Ro,max between 1.54 and 2.78%), and quantitative pore characterization experiments such as low-field nuclear magnetic resonance (LF-NMR) and low-temperature liquid nitrogen adsorption (LTN2A) were conducted. Based on multifractal theory, the heterogeneity law of pore structure was quantitatively evaluated, and its influencing factors were elucidated. The results showed that the BJH pore volume of coal samples in the study area ranged from 0.0005–0.0028 cm3/g, with an average of 0.0014 cm3/g, and the BET specific surface area was 0.07–2.52 m2/g, with an average of 0.41 m2/g. The NMR T2 spectrum peaked at 0.1–1, 10–100 and 100–1000 ms, and the spectrum was mostly bimodal or trimodal, indicating that pores of different pore sizes were developed. There were great differences in the pore structure of different coal ranks; high-rank coal was dominated by micropores, and the proportion of mesopores and macropores of medium-rank coal was higher. The pore structure of coal samples showed obvious multifractal characteristics, and the fractal characteristics of the sparse region (low-value information) were more significant; they dominated the pore distribution and had a stronger influence on the distribution of pore space. Pore structure heterogeneity is closely related to the degree of coalification, and with the increase in coalification, it is closely related to coal lithotype and quality, and high mineral and inertinite contents lead to the enhancement of pore structure heterogeneity in coal reservoirs, while Ro,max, Mad and vitrinite group contents have opposite effects. The research results provide theoretical guidance for the subsequent exploration and development of coalbed methane in the region.

Exploring Acute Changes in Hamstring EMG after Warm-up and Stretching Using a Multifractal Analysis.

This study aimed to apply multifractal detrended fluctuation analysis (MFDFA) to surface EMG to detect neuromuscular changes after realistic warm-up procedures that was followed by various stretching exercises. Sixteen volunteers conducted two experimental sessions. Testing included two maximal voluntary contractions before, after a standardized warm-up, and after a stretching exercise (static or neurodynamic nerve gliding technique). EMG was registered on biceps femoris and semitendinosus muscles. EMG was analyzed using different parameters obtained from the singularity Hurst exponent function and multifractal power spectrum (both obtained from the multifractal detrended fluctuation analysis). The Hurst exponent, α maximum, and peak value of the multifractal spectrum significantly decreased after warm-up as compared with baseline for both biceps femoris ( P = 0.003, P = 0.006, and P = 0.003, respectively) and semitendinosus ( P = 0.006, P = 0.013 and P = 0.01, respectively) muscles. No further alteration was obtained after static or neurodynamic nerve gliding stretching as compared with post-warm-up ( P = 1.0). No significant difference was obtained for Hurst exponent range, width, and asymmetry of the multifractal spectrum ( P > 0.05). From the present results, EMG depicted multifractal features sensitive to detect neuromuscular changes after a warm-up procedure. An increase in multiscale complexity is revealed after warm-up without any further alteration after stretching. The multifractal spectrum depicted dominant small fluctuations that shifted toward slightly larger fluctuations that could be attributed to motor unit recruitment.

The Dynamic Effects of COVID-19 and the March 2020 Crash on the Multifractality of NASDAQ Insurance Stock Markets

Triggered by COVID-19, one of the most dramatic crashes in the stock market in history occurred in March 2020. The sharp reductions in NASDAQ insurance stock indexes were observed after the occurrence of COVID-19 and in March 2020. In this study, the NASDAQ insurance stock markets (including NASDAQ Insurance Index, Developed Markets Insurance Index, and Emerging Markets Insurance Index) and NASDAQ Composite Index are utilized. The “scissors difference” between the NASDAQ Insurance Index and NASDAQ Composite Index is observed. The dynamic effects of the COVID-19 epidemic and the March 2020 crash on the multifractality of four series are explored. Firstly, the apparent and intrinsic multifractality, the components of multifractality, and the dynamic effects of the COVID-19 epidemic on these indexes are analyzed. Secondly, the multifractal cross-correlation between the NASDAQ Insurance Index and NASDAQ Composite Index is investigated. The dynamic influence of the COVID-19 epidemic on the cross-correlation is examined. The multifractal analysis results reveal that four series both before and after the occurrence of COVID-19 have multifractal characteristics. The stronger multifractal characteristics and the greater multifractal degree are obtained after the occurrence of COVID-19. The intrinsic multifractality of the three indexes ascends largely after the occurrence of COVID-19. The multifractal cross-correlation analysis illustrates that the cross-correlation between two indexes before and after the occurrence of COVID-19 is multifractal. The stronger multifractal cross-correlations and greater multifractal degrees are shown. The contribution of the intrinsic multifractal cross-correlation increased after the occurrence of COVID-19.

Performance improvement of MF-DFA on feature extraction of skin lesion images

In this paper, we propose an improved algorithm based on the original two-dimensional (2D) multifractal detrended fluctuation analysis (2D MF-DFA) that involves increasing the number of cumulative summations in the computational steps of 2D MF-DFA. The proposed method aims to modify the distribution of the generalized Hurst exponent to ensure that skin lesion image features are extracted based on enhanced multifractal features. We calculate the generalized Hurst exponent using 0, 1, or 2 cumulative summation processes. A support vector machine (SVM) is adopted to examine the classification performance under these three conditions. Computation shows that the process involving two cumulative summations achieves an accuracy, sensitivity, and specificity of [Formula: see text], [Formula: see text], and [Formula: see text], respectively, which indicates that its performance is much better than with 0 and 1 cumulative summations.

Islamic vs. Conventional Equity Markets: A Multifractal Cross-Correlation Analysis with Economic Policy Uncertainty

There is ample evidence that Islamic stock markets perform differently from conventional stock markets, particularly when economic policy uncertainty (EPU) or any other uncertainty such as geopolitical uncertainty is present. Considering this context, this paper examines the US EPU’s cross-correlation with both conventional and Islamic stock markets from the perspective of multifractality. Daily stock market prices of five main countries are considered: US, Thailand, Indonesia, Pakistan, and India. Using the multifractal detrended cross-correlation analysis (MF-DCCA), we validate the existence of long-range cross-correlation between US EPU and all the stock markets considered, demonstrating that all pairs of US EPU have strong power law and multifractal characteristics. Furthermore, all pairs display varying levels of multifractal strength, with the US EPU and US conventional stock market exhibiting the strongest multifractal patterns. Additionally, a cross-correlation between US EPU and the different stock markets is found to be persistent. The results of this study are pertinent to the various market participants in both conventional and Islamic markets, particularly investors, who may be able to draw useful conclusions from them for purposes such as portfolio diversification.

Operational parameters impact on spatial and temporal distribution and multifractal characteristics of particulate matter concentration under the sink effect

The influences of different factors on spatial and temporal mass transfer mechanism and dynamic characteristics of particulate matter (PM) under the sink effect are not clear. The objective of this study was to quantitatively analyze the influences of operational parameters on spatial and temporal distribution and multifractal characteristics of indoor suspended PM concentration under the sink effect. Results showed that with the increase of the applied voltage of the purification device, the reverse increase processes of PM1 and PM2.5 concentrations were progressively attenuated, and PM10 and total suspended particulates (TSP) concentrations decreased clearly. The dynamic evolution processes of the PM concentration series all presented strong persistence and obeyed the scale-invariant power-law statistical distributions. The positive correlation of the PM concentration series between five distances increased with the increase of applied voltage. This study can provide a reference basis for further refining the PM purification theory system under the sink effect.

Application of Multifractal Analysis Theory to Interpret T2 Cutoffs of NMR Logging Data: A Case Study of Coarse Clastic Rock Reservoirs in Southwestern Bozhong Sag, China

The Paleocene Kongdian Formation coarse clastic rock reservoir in Bozhong Sag is rich in oil and gas resources and has huge exploration potential. However, the coarse clastic rock reservoir has the characteristics of a complex pore structure and strong heterogeneity, which restrict the accuracy of evaluating the reservoir’s physical properties, such as porosity and permeability, for field evaluation. Nuclear magnetic resonance (NMR) technology has become a popular methods for unconventional reservoir evaluation because it can obtain abundant reservoir physical property information and because of its ability to identify fluid characteristics information. The transverse relaxation time (T2) cutoff (T2C) value is an important input parameter in the application of NMR technology. The accuracy of the T2C value affects the accuracy of the reservoir evaluation. The standard method for determining the T2C value requires a series of complicated centrifugation experiments in addition to the NMR experiments, and its application scope is limited by obtaining enough core samples. In this study, 14 core samples from the coarse clastic rock reservoir in the southwestern Bozhong sag of the Bohai Bay Basin were selected, and NMR measurements were carried out under the conditions of fully saturated water and irreducible water to determine the T2C value. Based on the multifractal theory, the NMR T2 spectrum of the saturated sample was analyzed, and the results show that the NMR T2 distribution of the saturated sample has multifractal characteristics, and the multifractal parameter Dq and the singular intensity range Δα have a strong correlation with the T2C value. Thus, based on multiple regression analyses of the multifractal parameters with the experimental T2C value of 10 core samples, we propose a method to predict the T2C value. After applying this method to 4 samples that were not used in the modeling, we confirmed that this method can be used to predict the T2C value of core samples. Furthermore, we expanded this method to the field application of a production well in Bozhong sag by adding an empirical index in the model. The new model can be used to directly calculate the T2C value of NMR logging data, and it does not require any other extra data, such as those from core analysis. This method is applicable in fast reservoir evaluations by only using NMR logging data in the field. The research results improve the accuracy of field NMR logging reservoir evaluations.

A NOVEL ECG AND EEG CLASSIFICATION SYSTEM BASED ON NONLINEAR STATISTICAL FEATURES

Accurate classification of the medical signals is urgently needed in clinical medicine. This paper aims to create a classifier to shorten the time of the classification and ensure the sorting accuracy, which assists physicians in saving diagnostic time and formulating the treatment plans. We create the classifier based on Kolmogorov complexity, Shannon entropy, Higuchi’s Hurst exponent and multifractal features. We obtain a feature value from Kolmogorov complexity, Shannon entropy and Higuchi’s Hurst exponent, and three feature values based on multifractal features to compose a vector and analyze it. Furthermore, we study a vector composed of six multifractal features as a control group. Electrocardiogram (ECG) and electroencephalogram (EEG) signals are applied to examine the performance of the classifier by support vector machine (SVM). The accuracy of ECG signals based on mixed classification (MC–ECG–SVM) reaches 94.17%, which is approximately 15% higher than that of ECG signals only based on multifractal features classification (UC–ECG–SVM). The sensitivities of MC–ECG–SVM and UC–ECG–SVM are 86.09% and 64.54%, respectively. The specificities of MC–ECG–SVM and UC–ECG–SVM are 98.26% and 93.65%, respectively. Analogously, the accuracy, sensitivity, and specificity of EEG signals based on mixed classification (MC–EEG–SVM) reach 95.29%, 96.28%, and 94.55%, respectively. The accuracy, sensitivity, and specificity of EEG signals based on multifractal features classification (UC–EEG–SVM) are 87.40%, 89.28%, and 88.11%, respectively. Therefore, the mixed classification method is more accurate than the classification method only based on multifractal features.

Chaotic Behavior Analysis and Multifractal Feature Learning of Specular Reflection Ionosphere Clutter for Target Detection

Because ionosphere condition is dynamically varying in the Earth’s middle-latitude, the long-range detection performance of operating high frequency surface wave radar (HFSWR) systems is severely restricted by the presence of ionosphere clutter. The development and performance evaluation of target detection under the F-layer specular reflection ionosphere clutter with concentrated power (Fs-concentrated clutter) will be described in this paper. First, this article pays attention to the variable chaotic behavior of Fs-concentrated clutter by using amplitude and phase echo data. Then, this article investigates the multifractal property of the power spectrum between the Fs-concentrated clutter and mixed echo component. The various fractal characteristics of different types of echo component and Doppler scale are analyzed. Next, the singularity intensity correlation function width, the accumulation area of multifractal correlation spectrum and asymmetry parameter are extracted as the learning features. These multifractal feature parameters are fed into the improved AlexNet and Resnet networks for distinguishing the types of echo component. Experimental results using real HFSWR echoes datasets have demonstrated that this proposed method can increase the detection probability by about 20% than the state-of-art detection methods and classical target detection methods under various signal-clutter ratio (SCR) background.